Question

Nonuniformball.
In the figure below, a ball of mass M andradius R
rolls smoothly from rest down a rampand onto a circular loop of
radius 0.51 m. The initial height of the ballis h = 0.33
m. At the loop bottom, the magnitude ofthe normal force on the ball
is 2.00Mg. The ball consistsof an outer spherical shell
(of a certain uniform density) that isglued to a central solid
sphere (of a different uniform density).The rotational inertia of
the ball can be expressed in the generalform I =
βMR2,but
β is not 0.4
asfor a ball with a single uniform density.Determine β.